(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The principal valueof the logarithmic function of a complex variable is defined to ave its argument in the range -pi < arg(z) < pi. By writing z = tan(w) in terms of exponentials, show that:

tan^{-1}(z) = (1/2i)ln[(1 + iz)/(1 - iz)]

3. The attempt at a solution

I have absolutely no idea where to start on this problem. My brain must be fried this week, but all I know how to do is write z = tan(w) in terms of exponentials.

z = (1/2i)(e^{iw}+ e^{-iw})/(e^{iw}- e^{iw})

Thanks!

Andrew

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# Homework Help: Complex Analysis and Trig

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